3D Time-of-flight distance measurement with custom - Universität ...
3D Time-of-flight distance measurement with custom - Universität ...
3D Time-of-flight distance measurement with custom - Universität ...
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86 CHAPTER 4<br />
Figure 4.1<br />
P<br />
lens<br />
Lambert reflector<br />
θ<br />
I ~ cos θ<br />
Lambert reflector.<br />
= P<br />
= P<br />
obj<br />
obj<br />
⋅<br />
2π<br />
θ<br />
⎛<br />
⋅ ⎜<br />
⎝<br />
∫ ∫<br />
0 0<br />
π<br />
2π<br />
2<br />
∫∫<br />
0 0<br />
2<br />
f<br />
R<br />
c<br />
⎞<br />
⎟<br />
⎠<br />
R<br />
cosθ<br />
⋅ sinθ<br />
dθ<br />
dϕ<br />
cosθ<br />
⋅ sinθ<br />
dθ<br />
dϕ<br />
⎛ 1 ⎞<br />
⋅ ⎜ ⎟<br />
⎝ 2 ⋅ F /# ⎠<br />
2<br />
= P<br />
2θc<br />
obj<br />
⋅<br />
( sinθ<br />
)<br />
OBJECTIVE<br />
c<br />
2<br />
= P<br />
obj<br />
D<br />
⎛ D ⎞<br />
⋅ ⎜ ⎟<br />
⎝ 2 ⋅ R ⎠<br />
2<br />
Equation 4.1<br />
With the reflection coefficient ρ <strong>of</strong> the object we can then calculate the power <strong>of</strong> the<br />
light source needed. These relationships are illustrated in Figure 4.2 and<br />
summarized in the following equations:<br />
Optical power per pixel Ppix (Apix is the light sensitive pixel area):<br />
⎛<br />
2 ⎞<br />
⎜<br />
⎛ D ⎞<br />
P<br />
⎟<br />
⎜ light source ⋅ ρ ⋅ ⎜ ⎟ ⋅ klens<br />
⎝ 2 ⋅ R ⎠ ⎟<br />
P pixel = ⎜<br />
⎟<br />
⎜<br />
A<br />
Equation 4.2<br />
image<br />
⎟<br />
⎜<br />
⎟<br />
⎝<br />
Apix<br />
⎠<br />
Expressed in terms <strong>of</strong> power density Pi’ (watts per square-meter) one obtains the<br />
simple relation:
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